Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16812044 | C2 | semidirect |
| 5. #20292386 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. #424×C107 | C2 | semidirect |
| 18. #16812032 | C4 | semidirect |
| 19. #16812032 | C4 | semidirect |
| 20. #16812029 | C4 | semidirect |
| 21. #16812029 | C4 | semidirect |
| 110. C107 | #1866 | semidirect |
| 113. #424 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812115 | 2 |
| C2×#16812044 | 2 |
| C2×#16812035 | 2 |
| #20292621 | 2 |
| #20292386 | 2 |
| #20292381 | 2 |
| #424×C107 | 2 |
| #1866 | 107 |